{"id":9524,"date":"2017-05-03T15:26:47","date_gmt":"2017-05-03T15:26:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9524"},"modified":"2017-12-08T19:41:06","modified_gmt":"2017-12-08T19:41:06","slug":"multiplying-and-dividing-mixed-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/multiplying-and-dividing-mixed-numbers\/","title":{"raw":"Multiplying and Dividing Mixed Numbers","rendered":"Multiplying and Dividing Mixed Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Multiply mixed numbers and fractions<\/li>\r\n \t<li>Divide an integer by a fraction<\/li>\r\n \t<li>Divide a mixed number by an integer<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the previous section, you learned how to multiply and divide fractions. All of the examples there used either proper or improper fractions. What happens when you are asked to multiply or divide mixed numbers? Remember that we can convert a mixed number to an improper fraction. And you learned how to do that in Visualize Fractions.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nMultiply: [latex]3\\Large\\frac{1}{3}\\cdot \\frac{5}{8}[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469856328\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3\\Large\\frac{1}{3}\\cdot \\frac{5}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert [latex]\\Large3\\frac{1}{3}[\/latex] to an improper fraction.<\/td>\r\n<td>[latex]\\Large\\frac{10}{3}\\cdot \\frac{5}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{10\\cdot 5}{3\\cdot 8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large\\frac{\\color{red}{2}\\cdot 5\\cdot 5}{3\\cdot \\color{red}{2} \\cdot 4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors.<\/td>\r\n<td>[latex]\\Large\\frac{5\\cdot 5}{3\\cdot 4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{25}{12}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nNotice that we left the answer as an improper fraction, [latex]\\Large\\frac{25}{12}[\/latex], and did not convert it to a mixed number. In algebra, it is preferable to write answers as improper fractions instead of mixed numbers. This avoids any possible confusion between [latex]2\\Large\\frac{1}{12}[\/latex] and [latex]2\\cdot\\Large\\frac{1}{12}[\/latex] (which are <em>not<\/em> equal!).\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question height=\"270\"]146092[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video for another example of how to multiply a mixed number by a fraction.\r\n\r\nhttps:\/\/youtu.be\/SvTd_ZxvqCM\r\n<div class=\"textbox shaded\">\r\n<h3>Multiply or divide mixed numbers<\/h3>\r\n<ol id=\"eip-id1168468257930\" class=\"stepwise\" data-number-style=\"arabic\">\r\n \t<li>Convert the mixed numbers to improper fractions.<\/li>\r\n \t<li>Follow the rules for fraction multiplication or division.<\/li>\r\n \t<li>Simplify if possible.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nMultiply, and write your answer in simplified form: [latex]2\\Large\\frac{4}{5}\\left(\\normalsize -1\\Large\\frac{7}{8}\\right)[\/latex]\r\n[reveal-answer q=\"859815\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"859815\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468531210\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]2\\Large\\frac{4}{5}\\left(\\normalsize -1\\Large\\frac{7}{8}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert mixed numbers to improper fractions.<\/td>\r\n<td>[latex]\\Large\\frac{14}{5}\\left(-\\frac{15}{8}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large-\\frac{14\\cdot 15}{5\\cdot 8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large-\\frac{\\color{red}{2} \\cdot 7\\cdot \\color{red}{5} \\cdot 3}{\\color{red}{5} \\cdot \\color{red}{2}\\cdot 4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors.<\/td>\r\n<td>[latex]\\Large-\\frac{7\\cdot 3}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large-\\frac{21}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146160[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to multiply mixed numbers that are negative.\r\n\r\nhttps:\/\/youtu.be\/ahTOIf0fkOc\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nDivide, and write your answer in simplified form: [latex]3\\Large\\frac{4}{7}\\normalsize\\div 5[\/latex]\r\n[reveal-answer q=\"69025\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"69025\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467104894\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3\\Large\\frac{4}{7}\\normalsize\\div 5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert mixed numbers to improper fractions.<\/td>\r\n<td>[latex]\\Large\\frac{25}{7}\\normalsize\\div\\Large\\frac{5}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\r\n<td>[latex]\\Large\\frac{25}{7}\\cdot \\frac{1}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{25\\cdot 1}{7\\cdot 5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large\\frac{\\color{red}{5} \\cdot 5\\cdot 1}{7\\cdot \\color{red}{5} }[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors.<\/td>\r\n<td>[latex]\\Large\\frac{5\\cdot 1}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{5}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146099[\/ohm_question]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nDivide: [latex]2\\Large\\frac{1}{2}\\normalsize\\div 1\\Large\\frac{1}{4}[\/latex]\r\n[reveal-answer q=\"403899\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"403899\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468240496\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]2\\Large\\frac{1}{2}\\normalsize\\div 1\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert mixed numbers to improper fractions.<\/td>\r\n<td>[latex]\\Large\\frac{5}{2}\\normalsize\\div\\Large\\frac{5}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\r\n<td>[latex]\\Large\\frac{5}{2}\\cdot \\frac{4}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{5\\cdot 4}{2\\cdot 5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large\\frac{\\color{red}{5} \\cdot \\color{red}{2} \\cdot 2}{\\color{red}{2} \\cdot 1\\cdot \\color{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors.<\/td>\r\n<td>[latex]\\Large\\frac{2}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146100[\/ohm_question]\r\n\r\n<\/div>\r\nThe next video provides several more examples of dividing mixed numbers, whole numbers and fractions.\r\n\r\nhttps:\/\/youtu.be\/zw7WdhQnXHw","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Multiply mixed numbers and fractions<\/li>\n<li>Divide an integer by a fraction<\/li>\n<li>Divide a mixed number by an integer<\/li>\n<\/ul>\n<\/div>\n<p>In the previous section, you learned how to multiply and divide fractions. All of the examples there used either proper or improper fractions. What happens when you are asked to multiply or divide mixed numbers? Remember that we can convert a mixed number to an improper fraction. And you learned how to do that in Visualize Fractions.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Multiply: [latex]3\\Large\\frac{1}{3}\\cdot \\frac{5}{8}[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168469856328\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3\\Large\\frac{1}{3}\\cdot \\frac{5}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert [latex]\\Large3\\frac{1}{3}[\/latex] to an improper fraction.<\/td>\n<td>[latex]\\Large\\frac{10}{3}\\cdot \\frac{5}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{10\\cdot 5}{3\\cdot 8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large\\frac{\\color{red}{2}\\cdot 5\\cdot 5}{3\\cdot \\color{red}{2} \\cdot 4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors.<\/td>\n<td>[latex]\\Large\\frac{5\\cdot 5}{3\\cdot 4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{25}{12}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Notice that we left the answer as an improper fraction, [latex]\\Large\\frac{25}{12}[\/latex], and did not convert it to a mixed number. In algebra, it is preferable to write answers as improper fractions instead of mixed numbers. This avoids any possible confusion between [latex]2\\Large\\frac{1}{12}[\/latex] and [latex]2\\cdot\\Large\\frac{1}{12}[\/latex] (which are <em>not<\/em> equal!).<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146092\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146092&theme=oea&iframe_resize_id=ohm146092&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video for another example of how to multiply a mixed number by a fraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Model the Product of a Fraction and Mixed Number Using Fraction Bars\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SvTd_ZxvqCM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox shaded\">\n<h3>Multiply or divide mixed numbers<\/h3>\n<ol id=\"eip-id1168468257930\" class=\"stepwise\" data-number-style=\"arabic\">\n<li>Convert the mixed numbers to improper fractions.<\/li>\n<li>Follow the rules for fraction multiplication or division.<\/li>\n<li>Simplify if possible.<\/li>\n<\/ol>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Multiply, and write your answer in simplified form: [latex]2\\Large\\frac{4}{5}\\left(\\normalsize -1\\Large\\frac{7}{8}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q859815\">Show Solution<\/span><\/p>\n<div id=\"q859815\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468531210\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>[latex]2\\Large\\frac{4}{5}\\left(\\normalsize -1\\Large\\frac{7}{8}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert mixed numbers to improper fractions.<\/td>\n<td>[latex]\\Large\\frac{14}{5}\\left(-\\frac{15}{8}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large-\\frac{14\\cdot 15}{5\\cdot 8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large-\\frac{\\color{red}{2} \\cdot 7\\cdot \\color{red}{5} \\cdot 3}{\\color{red}{5} \\cdot \\color{red}{2}\\cdot 4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors.<\/td>\n<td>[latex]\\Large-\\frac{7\\cdot 3}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large-\\frac{21}{4}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146160\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146160&theme=oea&iframe_resize_id=ohm146160&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to multiply mixed numbers that are negative.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 2:  Multiplying Signed Mixed Number\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ahTOIf0fkOc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Divide, and write your answer in simplified form: [latex]3\\Large\\frac{4}{7}\\normalsize\\div 5[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q69025\">Show Solution<\/span><\/p>\n<div id=\"q69025\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467104894\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3\\Large\\frac{4}{7}\\normalsize\\div 5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert mixed numbers to improper fractions.<\/td>\n<td>[latex]\\Large\\frac{25}{7}\\normalsize\\div\\Large\\frac{5}{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\n<td>[latex]\\Large\\frac{25}{7}\\cdot \\frac{1}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{25\\cdot 1}{7\\cdot 5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large\\frac{\\color{red}{5} \\cdot 5\\cdot 1}{7\\cdot \\color{red}{5} }[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors.<\/td>\n<td>[latex]\\Large\\frac{5\\cdot 1}{7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{5}{7}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146099\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146099&theme=oea&iframe_resize_id=ohm146099&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Divide: [latex]2\\Large\\frac{1}{2}\\normalsize\\div 1\\Large\\frac{1}{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q403899\">Show Solution<\/span><\/p>\n<div id=\"q403899\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468240496\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>[latex]2\\Large\\frac{1}{2}\\normalsize\\div 1\\Large\\frac{1}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert mixed numbers to improper fractions.<\/td>\n<td>[latex]\\Large\\frac{5}{2}\\normalsize\\div\\Large\\frac{5}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\n<td>[latex]\\Large\\frac{5}{2}\\cdot \\frac{4}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{5\\cdot 4}{2\\cdot 5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large\\frac{\\color{red}{5} \\cdot \\color{red}{2} \\cdot 2}{\\color{red}{2} \\cdot 1\\cdot \\color{red}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors.<\/td>\n<td>[latex]\\Large\\frac{2}{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]2[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146100\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146100&theme=oea&iframe_resize_id=ohm146100&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>The next video provides several more examples of dividing mixed numbers, whole numbers and fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Division of Fractions Using Formal Rules\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zw7WdhQnXHw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9524\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID: 146092, 146160, 146099, 146100. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Model the Product of a Fraction and Mixed Number Using Fraction Bars. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/SvTd_ZxvqCM\">https:\/\/youtu.be\/SvTd_ZxvqCM<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Division of Fractions Using Formal Rules. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zw7WdhQnXHw\">https:\/\/youtu.be\/zw7WdhQnXHw<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Model the Product of a Fraction and Mixed Number 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